The probability that a mother is a carrier is approximately 0.018.
The Hardy-Weinberg equilibrium formula can be used to determine the frequency of alleles in a population, as well as to make predictions about the probability of certain traits occurring in the next generation. In this case, we are interested in determining the probability that a mother is a carrier of a particular disease, given that the frequency of the disease is 1/4300.
To use the Hardy-Weinberg formula, we need to know the frequency of both the dominant and recessive alleles in the population. Assuming that the disease allele is recessive (i.e., carriers are heterozygous), we can represent the frequency of the disease allele (q) as
[tex]q = \sqrt{(1/4300)} = 0.004644.[/tex]
To determine the frequency of carriers (heterozygotes), we can use the formula p * q * 2,
where p represents the frequency of the dominant allele (which is equal to 1 - q in this case).
Therefore:
[tex]p = 1 - q \\ = 1 - 0.004644 = 0.995356\\q = \sqrt{(1/4300} = 0.004644\\p * q * 2 =0.018[/tex]
Approximately 1.8% of the population will be carriers of the disease allele. This means that the probability that a mother is a carrier is approximately 0.018.
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Gerald had some green and yellow beads. The number of green beads was 1/3 the number of yellow beads. He gave each of his friends 2 green beads and 3 yellow beads. He then had 42 green beads and 270 yellow beads left.
a. How many friends did he give the beads to?
b. What was the total number of beads he had at first?
Answer:
Step-by-step explanation:
Let's use algebra to solve this problem.
Let's start by assigning variables to the unknown quantities. Let G be the initial number of green beads and Y be the initial number of yellow beads.
We know that the number of green beads is 1/3 the number of yellow beads:
G = (1/3)Y
After giving away some beads, he had 42 green beads and 270 yellow beads left. So we can set up two equations using this information:
G - 2f = 42
Y - 3f = 270
where f is the number of friends he gave the beads to.
Now we can substitute G = (1/3)Y into the first equation:
(1/3)Y - 2f = 42
Multiplying both sides by 3, we get:
Y - 6f = 126
Now we have two equations that we can solve simultaneously:
Y - 3f = 270
Y - 6f = 126
Subtracting the first equation from the second, we get:
3f = 144
So f = 48. He gave the beads to 48 friends.
To find the total number of beads he had at first, we can use the equation G = (1/3)Y:
G + Y = (4/3)Y = (4/3)(270) = 360
So he had a total of 360 beads at first.
If 16% of a number is 40, find 4% of that number.
4% of a number is therefore 10, or 10 by Divide both sides of the equation by 0.16 and to determine the fourth percent of the number.
what is equation ?Typically, an equation consists of one or more variables, which might have varying values and are typically represented by letters. Equations are frequently used to explain relationships between distinct values or to address issues in a variety of fields. An example of an equation with one variable is x + 2 = 5. It denotes that x plus 2 add up to 5 in total.
given
With the provided data, we can first determine the complete number:
If 40 is 16% of a number, then the following equation may be written:
0.16x = 40
where x is the complete number that we are looking for.
Divide both sides of the equation by 0.16 to find the value of x:
x = 40/0.16
x = 250
Hence, the total is 250.
We can now utilise this knowledge to determine the fourth percent of the number:
4% of 250 is:
0.04 × 250 = 10
4% of a number is therefore 10, or 10 by Divide both sides of the equation by 0.16 and to determine the fourth percent of the number.
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in 1970, an industrial waste site contained an estimated 350 tons of contaminated soil. special cleaning crews were contracted to clean up the site. the crews can remove 20% of the contaminated soil each year. a. how do we know this describes an exponential function?
In 1970, an industrial waste site contained an estimated 350 tons of contaminated soil. special cleaning crews were contracted to clean up the site. the crews can remove 20% of the contaminated soil each year. describes an exponential function because it follows a fixed rate of decay over time, which can be expressed as a mathematical formula.
The given data describes an exponential function because it describes a quantity that decreases at a fixed rate over time.
The 350 tons of contaminated soil represents the initial quantity, and the special cleaning crews removing 20% of the contaminated soil each year represents the rate of decay. This decay rate can be expressed as a percentage decrease, which describes an exponential function.
To be more specific, an exponential function is a mathematical model that describes the decay of a quantity over a period of time. The decay rate can be expressed as a constant, which is multiplied by the initial quantity. The resulting value represents the quantity of the item at the end of each time period.
For example, in the given situation, the initial quantity of contaminated soil is 350 tons.
After one year, the quantity decreases by 20%, or 0.2, to represent the amount of contaminated soil removed.
This can be expressed as a mathematical formula as follows:
Q1 = 350 x 0.2
where Q1 is the quantity after the first year.
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City pollution in Singapore (scientific notation)?
According to the World Air Quality Report 2020, the annual average PM2.5 concentration in Singapore was 14.8 μg/m³ (micrograms per cubic meter which can be expressed in scientific notation as 1.48 x 10^-5 g/m³.
What is important fact on city pollution in Singapore?The PM2.5 concentration refers to fine particulate matter that can pose health risks when inhaled, and sources of such pollution in urban areas can include traffic, industrial activities, and power generation.
Despite its relatively low PM2.5 concentration compared to many other cities in the world, Singapore continues to work on improving air quality and reducing pollution through measures such as promoting the use of public transportation, implementing emission standards for vehicles, and encouraging the adoption of clean energy technologies.
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a researcher wishes to conduct a study of the color preferences of new car buyers. suppose that 30% of this population prefers the color green . if 16 buyers are randomly selected, what is the probability that at least 4 buyers would prefer green ? round your answer to the nearest ten-thousandth, if necessary.
The probability that at least 4 buyers would prefer green among the 16 selected is approximately 0.1031.
What is probability?
Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.
This problem can be modeled as a binomial distribution with n = 16 trials and p = 0.3 probability of success (preferring green).
Let X be the number of buyers who prefer green among the 16 selected. We need to find P(X ≥ 4).
Using a binomial probability table or calculator, we can find:
P(X ≥ 4) = 1 - P(X < 4)
= 1 - P(X ≤ 3)
= 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]
= 1 - [0.1233 + 0.2854 + 0.3028 + 0.1854]
= 0.1031 (rounded to 4 decimal places)
Therefore, the probability that at least 4 buyers would prefer green among the 16 selected is approximately 0.1031.
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there are 12 people in an office with 4 different phone lines. if all the lines begin to ring at once, how many groups of 4 people can answer these lines?
As per the combination method, there are 495 groups of 4 people that can answer the 4 different phone lines when there are 12 people in the office.
To start, we need to determine how many ways we can choose 4 people from a group of 12. We use the formula for combinations, which is:
ⁿCₓ = n! / x!(n-x)!
Where n is the total number of people (in this case, 12) and x is the number of people we want to choose (in this case, 4). The exclamation point symbol (!) denotes the factorial operation, which means we multiply the number by every positive integer less than it down to 1.
So, for this problem, we have:
¹²C₄ = 12! / 4!(12-4)!
= (12 x 11 x 10 x 9) / (4 x 3 x 2 x 1)
= 495
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Roy bought a board game for $22. Then, he marked up the price of the board game and resold it for $25.78. What percentage of the original price was the markup rate?
what is -4x+20≥28 i need to fast though
Answer:
[tex]x\leq -2[/tex]
Step-by-step explanation:
Solve for x:
[tex]-4x+20\geq 28[/tex]
Subtract 20 on both sides
[tex]-4x\geq 8[/tex]
Flip the sign and multiply both sides by -4
[tex]16x\leq -32[/tex]
Divide by 16
[tex]x\leq -2[/tex]
Write a proportion to determine the missing measure.
A lighthouse casts a 72-yard shadow at the same time as a 32-foot tall billboard casts a 19-foot shadow.
What is the height of the lighthouse?
A 121.3 yd
B 64.8 yd
C 42.8 yd
D 118.4 ft
Answer:
Step-by-step explanation:
First, we need to make sure that we are comparing the units in the same system, either yards or feet. Let's convert 32 feet to yards:
32 feet * 1 yard/3 feet = 10.67 yards
Now we have:
Lighthouse height / Lighthouse shadow = Billboard height / Billboard shadow
Let x be the height of the lighthouse in yards.
x / 72 yards = 10.67 yards / 19 feet
We can simplify the equation by converting everything to yards:
x / 72 = 10.67 / 3.28
x / 72 = 3.25
To solve for x, we can cross-multiply:
x = 72 * 3.25
x = 234
Therefore, the height of the lighthouse is 234 yards.
Answer: A) 121.3 yd.
each year a company selects a number of employees for a management training program. on average, 40 percent of those sent complete the program. out of the 23 people sent, what is the probability that exactly 7 complete the program?
The probability that exactly 7 employees out of 23 sent complete the program is 0.217 or 21.7%.
In this case, the number of trials is 23, and the probability of success is 0.4 (since, on average, 40% of those sent complete the program). We want to find the probability of exactly 7 successes.
The binomial probability formula is:
P(X=k) = [tex](^n_k) \times p^k \times (1-p)^{(n-k)}[/tex]
Where P(X=k) is the probability of k successes, n is the total number of trials, p is the probability of success, and (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials.
Using this formula, we can calculate the probability of exactly 7 employees completing the program as follows:
P(X=7) = [tex](^{23} _7) \times 0.4^7 \times (1-0.4)^{(23-7)}[/tex]
= 0.217 or 21.7%
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answer this for points please i need this done
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer... I think
15. Anna has $2.00 in change, including 5 quarters. What is the maximum number of dimes she can have? A 2 C 7 B 5 D 9
Answer:
To solve the problem, we need to first determine the value of the quarters Anna has. Since there are 5 quarters, we have:
5 quarters = 5 x $0.25 = $1.25
Thus, Anna has $2.00 - $1.25 = $0.75 left. We can find the maximum number of dimes she can have by dividing this amount by the value of a dime, which is $0.10. Therefore:
$0.75 ÷ $0.10 = 7.5
Since Anna cannot have a fraction of a dime, we round down to the nearest whole number to get a maximum of 7 dimes. Therefore, the answer is option B, 5.
Rachana has a set of ten mugs the set up is made of 3 different mugs
If Rachana randomly selects two mugs from the set, the probability that she gets two different mugs is 0.1556 or 15.56%.
To solve this problem, we can use the concept of combinations. Since there are 10 mugs in the set, there are 10 choose 2 = 45 ways to select two mugs without considering order.
Out of these 45 ways, we need to count the number of ways Rachana can select two different mugs. Since there are 3 different types of mugs, Rachana can choose any one of the three types for the first mug. There are 10 mugs in the set, out of which 3 belong to the chosen type. Therefore, the probability of choosing a mug of the chosen type is 3/10.
For the second mug, Rachana can choose from the remaining 9 mugs. Since she needs to choose a different type of mug, she can choose any one of the 2 remaining types. There are 7 mugs left from the other 2 types. Therefore, the probability of choosing a mug of a different type is (7/9) * 2/3 = 14/27.
Therefore, the probability of selecting two different mugs is the product of the probabilities of selecting a mug of the chosen type and a mug of a different type. This is given by (3/10) * (14/27) = 7/45, which is approximately 0.1556 or 15.56%.
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Complete question is:
Rachana has a set of ten mugs the set up is made of 3 different mugs. If Rachana randomly selects two mugs from the set, what is the probability that she gets two different mugs?
I NEED HELP ON THIS ASAP!!
A sports ticketing company offers two ticket plans. One plan costs $110 plus $25 per ticket. The other plan costs $40 per ticket. How many tickets must Gloria buy in order for the first plan to be the better buy?
Answer: Gloria must but at least one ticket in order for the first plan to be the better plan
What are linear and non-linear functions?
A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.
Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.
An example of a non-linear function is a quadratic function.
Given, A sports ticketing company offers two ticket plans. One costs $11 plus $25 per ticket and the other plan costs$40 per ticket.
Let, The number of tickets be 'x'.
Therefore, The number of tickets Gloria should buy so that the first plan is a better plan is,
11x + 25 < 40x.
11x - 40x < - 25.
- 29x < - 25.
29x > 25.
x > 25/29.
x > 0.86.
So, Gloria must buy at least 1 ticket.
Step-by-step explanation:
does anyone know the answer??
The point that partitions segment AB in a 1:4 ratio is (-1, -0.4).
How to determine the coordinates of point Q?In this scenario, line ratio would be used to determine the coordinates of the point Q on the directed line segment AB that partitions the segment into a ratio of 1 to 4.
In Mathematics, line ratio can be used to determine the coordinates of Q and this is modeled by the following mathematical expression:
Q(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Substituting the given parameters into the line ratio formula, we have;
Q(x, y) = [(1(7) + 4(-3))/(1 + 4)], [(1(-10) + 4(2))/(1 + 4)]
Q(x, y) = [(7 - 12)/(5)], [(-10 + 8)/5]
Q(x, y) = [-5/5], [(-2)/(5)]
Q(x, y) = [-1, -2/5]
Q(x, y) = [-1, -0.4]
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an expression for the length of one rectangle is . the length of a similar rectangle is expressed as
An expression for the length of one rectangle is the product of the ratio of the similar rectangle to the length of the original rectangle. The length of a similar rectangle is expressed as the same ratio.
The ratio of the length of the similar rectangle to the length of the original rectangle and the length of the original rectangle are used to calculate the length of a similar rectangle. For instance, if the original rectangle's length is 10 and the similar rectangle's length is 20, the length of the similar rectangle may be expressed as (20/10) × 10 = 20.
The comparable lengths of identical forms have the same ratio. It is possible to compute lengths using this fact. For instance, the corresponding sides of two rectangles are proportionate if they are identical.
The ratio of the lengths is 11/l2 if one rectangle has length 11 and the second rectangle has length 12. The ratio of the widths is the same if one rectangle has width w1 and the other has width w2, which is w1/w2.
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Correct question is:
An expression for the length of one rectangle is _____. The length of a similar rectangle is expressed as _____.
PLS HELP I NEED HELP ASAP
Answer:
3a + 2b
Step-by-step explanation:
The perimeter of the rectangle is calculated by following formula:
2×(w+l)
w: width, l: lengthLet x represent the missing side length, width,
2(x + 5a - b) = 16a + 2b
Multiply inside the parenthesis 22x + 10a - 2b = 16a + 2b
transfer 10a - 2b to the other side of the equation2x = 16a + 2b - 10a + 2b
Add/subtract like terms2x = 6a + 4b
Divide both sides by 2x = 3a + 2b
Help help help help help HELP ME PLEASE THIS IS DUE REALLY SOOONNN
answer for number 14 is 1115
you mutliply 27 into 1 ×45 into 100
it is 100 because we are dealing with percentage
so you say (write in fraction form)
27÷1×45÷100
=1215÷100
you get the answer of 1115
so there were 1115 female butterflies
we can subtract the answer from the original number to get the number of male butterflies
1215-1115 =100 male butterflies
3 Which of the following figures have
the same area?
2.9 cm
II
4 cm
2 cm
A. Figures I and II
C. Figures I and III
I
5.8 cm
III 3.7 cm
3.7 cm
B. Figure II and III
D. None of the above
We can see here that the figures that have the same area are: A. Figures I and II.
What is area?Area is a measure of the size of a two-dimensional surface or shape. It refers to the amount of space inside the boundaries of a flat object, such as a rectangle, triangle, or circle. Area is typically measured in square units, such as square meters, square feet, or square centimeters.
The area of Figure I which is a rectangle is = l × b = 2cm × 5.8cm = 11.6cm².
The area of Figure II which is a parallelogram is = b × h = 4cm × 2.9cm = 11.6cm².
Thus, Figures I and II have the same area.
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if she picks another 250 balls at random, how many red balls should she expect
Answer:
Step-by-step explanation:
250
I NEED HELP PLEASE!!!
I have no idea, good luck though pal
Step-by-step explanation:
You
Got
This
<3
Please I really need the help I only have 30 minutes left this is my second attempt at this
The correct option is the second one, your supervisor did not divide by the total number of bags.
What mistake did your supervisor did?Here we can see a table with the size of each bag (in grams) and the number of sold bags.
Now, remember that for a set of N numbers {x₁, ..., xₙ} the mean is:
M = (x₁ + x₂ + ...)/N
So the denominator is the amount of elements in the set.
Then here in the denominator we should see the total number of bags sold, which is:
25 + 32 + 40 + 18 = 115
That number should be in the denominator instead of the sum of the masses.
Then the correct option is the second one.
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an actuary has discovered that policyholders are three times as likely to file two claims as to file four claims. if the number of claims filed has a poisson distribution, what is the standard deviation of the number of claims filed?
The standard deviation of the number of claims filed, in this case, is equal to 1.732. This is an important metric for the actuary, as it provides an indication of how much variation there is in the number of claims filed.
The standard deviation of the number of claims filed is equal to the square root of the mean. In this case, the mean is equal to three. Thus, the standard deviation of the number of claims filed is equal to the square root of three, which is equal to 1.732.
To explain further, the Poisson distribution is a discrete probability distribution that is used to calculate the probability of a certain number of events occurring within a given time interval. It is based on the assumption that these events occur independently and at a constant rate. In this case, the rate is equal to the mean, which is equal to three. Thus, the standard deviation is equal to the square root of the mean.
The standard deviation of the number of claims filed is an important metric for the actuary, as it provides an indication of how much variation there is in the number of claims filed. The larger the standard deviation, the greater the amount of variation, and vice versa. In this case, the standard deviation is relatively low, which suggests that the number of claims filed is relatively consistent.
In conclusion, the standard deviation of the number of claims filed, in this case, is equal to 1.732. This is an important metric for the actuary, as it provides an indication of how much variation there is in the number of claims filed.
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find sin A 97, 72,65
Therefore, sin(A) is approximately 0.6708 (rounded to four decimal places).
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems related to geometry, physics, engineering, and many other fields. Trigonometry is based on the study of the six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions describe the ratios of the lengths of the sides of a right triangle, and can be used to calculate the unknown side lengths or angles of a triangle. Trigonometry is also useful for working with periodic functions, such as waves and oscillations. The trigonometric functions can be used to model and analyze these periodic phenomena, and to predict future behavior based on past observations. Applications of trigonometry can be found in many areas of science, engineering, and technology, including astronomy, navigation, architecture, surveying, and electronics.
Here,
To find sin(A), we need to use the trigonometric ratios of the sides of the right triangle ABC, where angle A is opposite to side a, angle B is opposite to side b and angle C is opposite to side c. We have sides of the triangle as follows:
a = 72
b = 65
c = 97
To find sin(A), we can use the following formula:
sin(A) = opposite/hypotenuse
In this case, the opposite side of angle A is b and the hypotenuse is c, so we have:
sin(A) = b/c
sin(A) = 65/97
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Complete question:
Find sin(A) when we have sides of the triangle as follows:
a = 72
b = 65
c = 97
Are the ratios 4:3 and 5:4 equivalent?
Answer:
They're not promise
Step-by-step explanation:
I did it on the calculator
I hope this helps youuu
Have a good day <3
. if an m-by-n matrix a multiplies an n-dimensional vector x, how many separate multiplications are involved? what if a multiplies an n-by-p matrix b?
If a multiplies an n x p matrix b then the total number of multiplications involved is m x p. And is given by Dimensional vector.
For explanation, There are two separate cases to consider when multiplying an m-by-n matrix and an n-dimensional vector, or an m-by-n matrix and an n-by-p matrix.
When an m-by-n matrix, A, multiplies an n-dimensional vector, x, the number of separate multiplications involved is m. This is because in order to compute the dot product of A and x, each row of A needs to be multiplied by the vector x, resulting in m separate multiplications.
On the other hand, when A multiplies an n-by-p matrix, B, the number of separate multiplications involved is m x p. This is because in order to multiply A and B, each row of A must be multiplied by each column of B, resulting in m x p separate multiplications.
Therefore, the number of separate multiplications involved when multiplying an m-by-n matrix and an n-dimensional vector is m, and the number of separate multiplications involved when multiplying an m x n matrix and an n x p matrix is m x p.
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PLEASE ANSWER AS QUICKLY AS YOU CAN!!!!!!
Answer:
(x+6)(x+6)
[tex]x^2+12x+36[/tex]
(x+8)(x-5)
[tex]x^{2}+3x-40\\[/tex]
(x-5)(x-2)
[tex]x^{2}-7x+10[/tex]
Step-by-step explanation:
Brainliest pls hope it helped^^
Answer:
a) x^(2)+12x+36
b) x^(2)+3x-40
c) x^(2)-7x+10
Step-by-step explanation:
now suppose that you are given samples -500, -499, -497, -496, 495, 497, 510. what would be your mle of the mean, assuming that the distribution is laplacian with scale 1? what if you assume that the scale is 500? does this seem reasonable?
MLE of the mean = -71.29.
To find the maximum likelihood estimator (MLE) for the mean of the given samples assuming a what if you assume that the scale is 500? does this seem reasonable? with scale 1, you need to calculate the sample mean, which is the average of all the samples.
This can be calculated by taking the sum of all the values divided by the number of samples. In this case,
the sum of all the samples is -499 and the number of samples is 7, so the sample mean is -499/7 = -71.29.
If you assume the scale is 500, the MLE of the mean will remain the same. However, it does not necessarily make sense to assume a Laplacian distribution with scale 500 since Laplacian distributions usually have a scale parameter between 0 and 1.
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Dina’s Ice Cream Shop sells only chocolate and vanilla ice cream. Each week, Dina puts either chocolate ice cream or vanilla ice cream on sale. She is trying to figure out which ice cream she should put on sale this week. Dina gets all of her business from people who walk by her ice cream shop and stop in. She performs some market research and asks 100 100100 different people if they would purchase chocolate ice cream, vanilla ice cream, or no ice cream if they walked by and chocolate ice cream was on sale. She does the same for vanilla ice cream being on sale.
Based on the market research, Dina can determine which ice cream flavor she should put on sale this week by comparing the number of people who would purchase each flavor if it was on sale.
How can she do this?For example, if 70 people said they would purchase chocolate ice cream if it was on sale and only 30 people said they would purchase vanilla ice cream if it was on sale, then Dina should put chocolate ice cream on sale this week.
On the other hand, if 60 people said they would purchase vanilla ice cream if it was on sale and only 40 people said they would purchase chocolate ice cream if it was on sale, then Dina should put vanilla ice cream on sale this week.
It's important to note that Dina's market research only represents a sample of people who walk by her ice cream shop and stop in. It may not be representative of the entire population of potential customers. Therefore, Dina should take this into account when making her decision.
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Figure LMNOPQRS is a regular octagon. Segment LS is located at L (0, 0) and S (0, 1). What is the perimeter of LMNOPQRS?
A. 8 units
B. 10 units
C. 12 units
D. 14 units
The perimeter of the given regular octagon is 8 units.
What is the perimeter of a regular polygon?
The perimeter of a regular polygon is the total length of its sides, and for a regular octagon, it is given by the formula [tex]P = 8s[/tex] , where s is the value of each side. To find the length of each side, we can use the coordinates of two adjacent vertices of the octagon.
Calculating the value of the perimeter :
In this question, we are given that the octagon is regular and that segment LS is located at L (0,0) and S (0,1).
To find the perimeter of the octagon, we can use the formula [tex]P = 8s,[/tex], where s is the value of each side.
We can find the length of each side by using the coordinates of two adjacent vertices of the octagon. Let us consider the coordinates of vertices L and M. The distance between L and M can be calculated using the distance formula as follows:
[tex]d =\sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}[/tex]
where [tex](x_1, y_1) = (0, 0)[/tex]and [tex](x_2, y_2) = (1, 0)[/tex]
[tex]d = \sqrt{((1 - 0)^2 + (0 - 0)^2)}= 1[/tex]
Therefore, the length of each side of the octagon is 1 unit.
Substituting s = 1 unit in the formula for the perimeter of the octagon, we get:
[tex]P = 8s = 8(1) = 8[/tex] units
Hence, the perimeter of the given regular octagon is 8 units.
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